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# 644 (number)

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### 644 (number)

For the years 600, see 600s BC (decade) and 600.

600 (six hundred) is the natural number following 599 and preceding 601.

## Mathematical properties

Six hundred is a composite number, an abundant number, a pronic number and a Harshad number.

## In other fields

• In the United States, a credit score of 600 or below is considered a poor score, thus limiting available credit (or requiring the borrower to pay higher interest rates).
• 600 is also the advertised number of miles that NASCAR runs in the Coca-Cola 600, the longest race on any of the NASCAR circuits.
• Fiat 600

## Integers from 601 to 699

### 600s

601 prime number, centered pentagonal number

602 = 2 × 7 × 43, nontotient, area code for Phoenix, AZ along with 480 and 623

603 = 32 × 67, Harshad number, area code for New Hampshire

604 = 22 × 151, nontotient, totient sum for first 44 integers, area code for southwestern British Columbia (Lower Mainland, Fraser Valley, Sunshine Coast and Sea to Sky)

605 = 5 × 112, Harshad number

606 = 2 × 3 × 101, sphenic number, sum of six consecutive primes (89 + 97 + 101 + 103 + 107 + 109)

607 prime number, sum of three consecutive primes (197 + 199 + 211), Mertens function(607) = 0, balanced prime, strictly non-palindromic number

608 = 25 × 19, Mertens function(608) = 0, nontotient

609 = 3 × 7 × 29, sphenic number

### 610s

610 = 2 × 5 × 61, sphenic number, nontotient, Fibonacci number, Markov number. Also a kind of telephone wall socket used in Australia. China's 6-10 office (also called 610 office) is an extra-constitutional Gestapo-like organisation established to persecute practitioners of Falun Gong.

611 = 13 × 47

612 = 22 × 32 × 17, Harshad number, area code for Minneapolis, MN

613 = Primes: prime number, first number of prime triple (p, p + 4, p + 6), middle number of sexy prime triple (p − 6, p, p + 6). Geometrical numbers: Centered square number with 18 per side, circular number of 21 with a square grid and 27 using a triangular grid. Also 17-gonal. Hypotenuse of a right triangle with integral sides, these being 35 and 612. Partitioning: 613 partitions of 47 into non-factor primes, 613 non-squashing partitions into distinct parts of the number 54. Squares: Sum of squares of two consecutive integers, 17 and 18. Additional properties: a lucky number.

In Judaism the number 613 is very significant, as its metaphysics, the Kabbalah, views every complete entity as divisible into 613 parts: 613 parts of every Sefirah; 613 mitzvot, or divine Commandments in the Torah; 613 parts of the human body.

The number 613 hangs from the rafters at Madison Square Garden in honor of legendary New York Knicks coach Red Holzman's 613 victories.

614 = 2 × 307, nontotient

According to Rabbi Emil Fackenheim, the number of Commandments in Judaism should be 614 rather than the traditional 613.

615 = 3 × 5 × 41, sphenic number

616 = 23 × 7 × 11, Padovan number, an alternative value for the Number of the Beast (more commonly accepted to be 666).

617 prime number, sum of five consecutive primes (109 + 113 + 127 + 131 + 137), Chen prime, Eisenstein prime with no imaginary part

618 = 2 × 3 × 103, sphenic number

619 prime number, strobogrammatic prime, alternating factorial

### 620s

620 = 22 × 5 × 31, sum of four consecutive primes (149 + 151 + 157 + 163), sum of eight consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97)

621 = 33 × 23, Harshad number

622 = 2 × 311, nontotient

It is also the standard diameter of modern road bicycle wheels (622 mm, from hook bead to hook bead)

623 = 7 × 89

624 = 24 × 3 × 13, sum of a twin prime (311 + 313), Harshad number, Zuckerman number

625 = 54 = 252, sum of seven consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103), centered octagonal number, 1-automorphic number, Friedman number since 625 = 56−2

626 = 2 × 313, nontotient

627 = 3 × 11 × 19, sphenic number, number of integer partitions of 20, Smith number

628 = 22 × 157, nontotient, totient sum for first 45 integers

629 = 17 × 37, highly cototient number, Harshad number

### 630s

630 = 2 × 32 × 5 × 7, sum of six consecutive primes (97 + 101 + 103 + 107 + 109 + 113), triangular number, hexagonal number, sparsely totient number, Harshad number

631 prime number, centered triangular number, centered hexagonal number, Chen prime

632 = 23 × 79

633 = 3 × 211, sum of three consecutive primes (199 + 211 + 223); also, in the title of the movie 633 Squadron

634 = 2 × 317, nontotient, Smith number

635 = 5 × 127, sum of nine consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89), Mertens function(635) = 0.

"Project 635", the Irtysh River diversion project in China involving a dam and a canal.

636 = 22 × 3 × 53, sum of ten consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83), Smith number, Mertens function(636) = 0,

637 = 72 × 13, Mertens function(637) = 0, decagonal number

638 = 2 × 11 × 29, sphenic number, sum of four consecutive primes (151 + 157 + 163 + 167), nontotient, centered heptagonal number

639 = 32 × 71, sum of the first twenty primes, also ISO 639 is the ISO's standard for codes for the representation of languages

### 640s

640 = 27 × 5, Harshad number

641 prime number, Sophie Germain prime, factor of 4294967297 (the smallest nonprime Fermat number), Chen prime, Eisenstein prime with no imaginary part, Proth prime

642 = 2 × 3 × 107, sphenic number

643 prime number, largest prime factor of 123456

644 = 22 × 7 × 23, nontotient, Perrin number. Harshad number, common umask.

645 = 3 × 5 × 43, sphenic number, Smith number, Fermat pseudoprime to base 2, Harshad number

646 = 2 × 17 × 19, sphenic number, also ISO 646 is the ISO's standard for international 7-bit variants of ASCII

647 prime number, sum of five consecutive primes (113 + 127 + 131 + 137 + 139), Chen prime, Eisenstein prime with no imaginary part

648 = 23 × 34, Harshad number

649 = 11 × 59, number of total Pokémon species as of Pokémon Black and White

### 650s

650 = 2 × 52 × 13, primitive abundant number, square pyramidal number, pronic number, nontotient, totient sum for first 46 integers

651 = 3 × 7 × 31, sphenic number, pentagonal number, nonagonal number

652 = 22 × 163

653 prime number, Sophie Germain prime, balanced prime, Chen prime, Eisenstein prime with no imaginary part

654 = 2 × 3 × 109, sphenic number, nontotient, Smith number

655 = 5 × 131

656 = 24 × 41

657 = 32 × 73, probably the largest number not of the form a2+s with s a semiprime

658 = 2 × 7 × 47, sphenic number

659 prime number, Sophie Germain prime, sum of seven consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107), Chen prime, Mertens function sets new low of −10 which stands until 661, highly cototient number, Eisenstein prime with no imaginary part, strictly non-palindromic number

### 660s

660 = 22 × 3 × 5 × 11, sum of four consecutive primes (157 + 163 + 167 + 173), sum of six consecutive primes (101 + 103 + 107 + 109 + 113 + 127), sum of eight consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101), sparsely totient number, Harshad number

661 prime number, sum of three consecutive primes (211 + 223 + 227), Mertens function sets new low of −11 which stands until 665, star number

662 = 2 × 331, nontotient, member of Mian–Chowla sequence

663 = 3 × 13 × 17, sphenic number, Smith number

664 = 23 × 83

665 = 5 × 7 × 19, sphenic number, Mertens function sets new low of −12 which stands until 1105

666: See 666 (number)

667 = 23 × 29

668 = 22 × 167, nontotient

669 = 3 × 223

### 670s

670 = 2 × 5 × 67, sphenic number, octahedral number, nontotient

671 = 11 × 61

This number is the magic constant of n×n normal magic square and n-queens problem for n = 11.

672 = 25 × 3 × 7, harmonic divisor number, Zuckerman number,

track 5 of The Dresden Dolls.

673 prime number, Proth prime

674 = 2 × 337, nontotient

675 = 33 × 52

676 = 22 × 132 = 262

677 prime number, Chen prime, Eisenstein prime with no imaginary part

678 = 2 × 3 × 113, sphenic number, nontotient

679 = 7 × 97, sum of three consecutive primes (223 + 227 + 229), sum of nine consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97)

### 680s

680 = 23 × 5 × 17, tetrahedral number, nontotient

681 = 3 × 227, centered pentagonal number

682 = 2 × 11 × 31, sphenic number, sum of four consecutive primes (163 + 167 + 173 + 179), sum of ten consecutive primes (47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89)

683 prime number, Sophie Germain prime, sum of five consecutive primes (127 + 131 + 137 + 139 + 149), Chen prime, Eisenstein prime with no imaginary part, Wagstaff prime

684 = 22 × 32 × 19, Harshad number

685 = 5 × 137, centered square number

686 = 2 × 73, nontotient, The code for international direct dial phone calls to Kiribati. 686 is name of company for snowboarding apparel.

687 = 3 × 229

688 = 24 × 43, Friedman number since 688 = 8 × 86

689 = 13 × 53, sum of three consecutive primes (227 + 229 + 233), sum of seven consecutive primes (83 + 89 + 97 + 101 + 103 + 107 + 109)

### 690s

690 = 2 × 3 × 5 × 23, sum of six consecutive primes (103 + 107 + 109 + 113 + 127 + 131), sparsely totient number, Smith number, Harshad number

ISO 690 is the ISO's standard for bibliographic references

691 prime number, (negative) numerator of the Bernoulli number B12 = -691/2730. Ramanujan's tau function τ and the divisor function σ11 are related by the remarkable congruence τ(n) ≡ σ11(n) (mod 691). In number theory, 691 is a "marker" (similar to the radioactive markers in biology): whenever it appears in a computation, one can be sure that Bernoulli numbers are involved.

692 = 22 × 173

693 = 32 × 7 × 11, the number of the "non-existing" Alabama State Constitution amendment, the number of sections in Ludwig Wittgenstein's Philosophical Investigations.

694 = 2 × 347, centered triangular number, nontotient

695 = 5 × 139

696 = 23 × 3 × 29, sum of eight consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), totient sum for first 47 integers

697 = 17 × 41

698 = 2 × 349, nontotient

699 = 3 × 233

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